The present invention relates to methods for determining geologic formation information using acoustic techniques. Specifically, the present invention relates to acoustic methods for determining information about the stress field in a geologic formation.
Acoustic Wavefields
Knowledge of characteristics of geologic formations is important for many industries. Such industries include petroleum exploration and development. Many methods have been developed for gathering such information. Some of these methods of characterizing geologic formations use acoustical means to gather that information. Typically in these methods, acoustic wavefields are transmitted into the formations. Some information about the formations is based on the fact that acoustic wavefields propagate at different speeds depending on the media.
However, acoustic wavefields not only propagate at different speeds depending on the media, but also propagate through elastic media in different modes. The modes include Compressional or P-waves, wherein particle motion is in the direction of wave travel; and transverse shear or S-waves, which assuming a homogeneous, isotropic medium, may be polarized in two orthogonal directions, with motion perpendicular to the direction of wave travel. There also exist asymmetrical flexural waves as will be discussed later.
P-waves propagate through both fluids and solids. Shear-waves cannot exist in a fluid. Compressional waves propagating through the borehole fluid may be mode-converted to shear-waves in the borehole sidewall material by Snell's law of refraction provided the shear-wave velocity of that material is greater than the compressional-wave velocity of the borehole fluids. If that is not true, then shear-waves in the sidewall material can be generated only by direct excitation.
Flexural waves are bending waves. Flexural waves involve substantial displacements of particles in the medium in a direction transverse to the direction of propagation, but flexural waves can neither be classified as compressional nor as transverse. The transverse impedance (resistance to propagation of the wave) of structures carrying bending waves can be of similar magnitude to that of sound waves in the adjacent fluid, thereby facilitating energy exchange between the two media.
Among other parameters, the various modes of propagation are distinguishable by their relative velocities. The velocity of compressional and transverse shear-waves is a function of the elastic constants and the density of the medium through which the waves travel. The S-wave velocity is, for practical purposes, about half that of P-waves. Compressional wavefields propagating through the borehole fluid are usually slower than formational shear-waves but for boreholes drilled into certain types of soft formations, the borehole fluid velocity may be greater than the sidewall formation S-wave velocity. The velocity of flexural waves is said to approach the S-wave velocity as an inverse function of the acoustic excitation frequency. Some authors refer to flexural waves as dipole shear-waves.
Acoustic Logging Tools
Acoustic logging tools for measuring properties of the sidewall material of both cased and uncased boreholes are well known. Essentially, such tools measure the travel time of an acoustic pulse propagating through the sidewall material over a known distance. In some studies, the amplitude and frequency of the acoustic pulse, after passage through the earth, are of interest.
In its simplest form, an acoustic logger consists of one or more transmitter transducers that periodically emit an acoustic pulse into the formation around the borehole. One or more receiver transducers, spaced apart by a known distance from the transmitter, detects the pulse after passage through the surrounding formation. The difference in time between pulse transmission and pulse reception divided into the distance between the transducers is the formation velocity. If the transducers do not contact the borehole sidewall, allowance must be made for time delays through the borehole fluid.
Acoustic Monopole/Dipole Well Logging Instruments
Acoustic monopole/dipole well logging instruments are used, among other purposes, for making measurements related to the shear propagation velocity and the compressional propagation velocity of earth formations penetrated by a wellbore. An acoustic well logging tool is generally cylindrically shaped and suitably sized for passage through a fluid filled well bore. Normally, the tool carries two or more transducers which are disposed and secured at a fixed distance from one another. In a typical acoustic tool an array of transducers serve as transmitters of sound waves while another array of transducers serve as receivers of sound waves. The receivers are spaced from one another at a predetermined distance and are disposed to one side of the transmitter along the longitudinal axis of the tool. In operation, the transmitter in the tool is electrically actuated periodically to emit pulses of acoustic energy (or pressure waves) which propagate outwardly from the transmitter with a velocity dependent upon the media traversed by the energy. The arrival of the acoustic energy at the successively positioned receivers is detected to trigger electrical circuits in the tool which function to ascertain a characteristic of the formation from the pulse of acoustic energy traveling the predetermined distance between the array receivers.
In a typical well bore, an acoustic tool is commonly spaced from the wall of the well bore so that the emitted acoustic wave energy or pressure pulses are first omnidirectionally (monopole) or unidirectionally (dipole) transmitted through fluid (usually mud) in the well bore and, after traveling through the fluid over the distance from the tool to the wall of the well bore, a portion of the traveling wave energy is transmitted to adjacent media surrounding the well bore. The characteristic velocity of wave motion or the wave energy through the fluids in the well is generally in the neighborhood of 5000 feet per second, while the characteristic velocity of wave motion through the adjacent media may vary from 5000 feet per second to 25,000 feet per second for compressional waves depending upon the type of media encountered. Other wave types have similar properties.
The portion of the acoustic wave energy transmitted into the media generally travels at a higher velocity than the corresponding portion of the wave energy traveling in the well bore fluid. Because of this, the portion of the wave energy traveling through media reaches a receiver prior to the time that the portion of the acoustic wave energy traveling through the fluids does. It is this feature of higher media velocity which permits measurement of the velocity of acoustic energy in the media surrounding a well bore.
Formation Stress Field
Detailed information regarding the formation stress field is very important for oil field operations. Stress controls the integrity/stability of rock formations of finite strength. Thus knowing the stress orientation and magnitude will help design drilling programs to avoid borehole instability or collapse. In reservoir engineering, knowing that stress will or will not cause borehole instability helps in making the decision of whether or not an expensive treatment (such as gravel packing) is necessary. Furthermore, knowledge of stress helps find the hydraulic fracture direction and helps determine the fluid flow direction in the reservoir. These are only a few examples illustrating the importance of knowing the formation stress field.
Traditionally, the measurement of in-situ stress has been performed using a borehole packer and microfracture test. This method is usually time-consuming and expensive. Determination of an in-situ stress field based on borehole acoustic measurements would provide a fast and inexpensive way of gathering detailed information for the formation stress field.
One proposed method for using acoustic measurements to determine information about the formation stress field is described by U.S. Pat. No. 4,641,520 issued to Mao. In the method of Mao, in-situ stresses are determined by measuring stress-induced shear-wave velocity anisotropy around and near a borehole using acoustic shear-waves. An estimation of the stress field is based on the fact that the difference between two shear-wave velocities is proportional to the stress difference in the two directions of particle motion.
Another proposed method for using acoustic measurements to determine information about the formation stress field is described by U.S. Pat. No. 5,298,215 issued to Sinha et al. In this method, low and high frequency flexural waves are generated with dipole transducers. From measurements made at receiving transducers which are oriented at two orthogonal directions in a horizontal plane normal to the borehole axis, and via known processing techniques, the received signals are transformed into arrivals as a function of frequency such that the principal polarization directions and the magnitudes of the maximum and minimum wave velocities at those directions are determined at different frequencies. Determination of whether uniaxial stress in the formation is attributed to stress induced azimuthal anisotropy (differences in the orientation of parameters such as permeability that vary angularly around the borehole that results from stress) as opposed to an intrinsic anisotropy (anisotropy that is intrinsic to the formation and not a result of stress) in the formation is deduced from comparison of the directions of the maximum and minimum shear-wave velocities of the low and high frequency waves. Then, the low frequency information is utilized to obtain values for a formation shear stress parameter.
Both of these techniques are based on the stress effect on shear-wave velocities. The technique of Mao uses a linear relation between stress and velocity while the technique of Sinha et al. utilizes a nonlinear relation for the stress and velocity. However, both of these techniques have substantial drawbacks. Some of the drawbacks of the technique of Mao are the fact that only velocity changes around and near the borehole are measured and the fact that the stress-velocity coupling coefficients are unknown parameters in the relation. Some of the drawbacks of the technique of Sinha et al. are the fact that it requires determining the nonlinear elastic constants and that it detects the stress-induced anisotropy using the cross-over phenomenon of the fast and slow dipole-shear-wave dispersion curves at high frequencies. This cross-over phenomenon may be difficult to observe for commonly observed anisotropy values of only a few percent. Furthermore, in both techniques, the influence of borehole pressure on the formation shear velocity is not considered. as will be shown, this pressure can significantly affect monopole shear-waves that can be used to identify the stress-induced anisotropy.